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  • Open Access

    ARTICLE

    Numerical Solution of Fractional Fredholm-Volterra Integro-Differential Equations by Means of Generalized Hat Functions Method

    Baofeng Li 1

    CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.2, pp. 105-122, 2014, DOI:10.3970/cmes.2014.099.105

    Abstract In this paper, operational matrix method based on the generalized hat functions is introduced for the approximate solutions of linear and nonlinear fractional integro-differential equations. The fractional order generalized hat functions operational matrix of integration is also introduced. The linear and nonlinear fractional integro-differential equations are transformed into a system of algebraic equations. In addition, the method is presented with error analysis. Numerical examples are included to demonstrate the validity and applicability of the approach. More >

  • Open Access

    ARTICLE

    Numerical Analysis on Dual Holes Interactions

    C. K. Chen1

    CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.3, pp. 221-234, 2013, DOI:10.3970/cmes.2013.093.221

    Abstract By extending Bückner’s superposition principle and alternating iteration method, this presentation studies the dual holes interactions. A newly developed numerical scheme is embedded in the conventional Gauss-Legendre quadrature routine for evaluating the boundary integral holding stress singularities. This developed scheme can avoid numerical singularity and facilitate the achieved stress field to be exact as that of analytical solution; however the chosen Gaussian integration points must enter a large quantity. This presentation uses an infinite plate with a centered hole strained by remote axial loading as a testing example, and the numerical results are capable of reaching the analytical solution in… More >

  • Open Access

    ARTICLE

    An alternating finite difference material point method for numerical simulation of high explosive explosion problems

    X. X. Cui1, X. Zhang1,2, K. Y. Sze3, X. Zhou4

    CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.5, pp. 507-538, 2013, DOI:10.3970/cmes.2013.092.507

    Abstract Based on the material point method (MPM), an alternating finite difference material point (AFDMP) method is proposed for modeling the 3D high explosive (HE) explosion and its interaction with structures nearby. The initiatory detonation and eventual fluid structure interaction (FSI) are simulated by the standard MPM. On the other hand, the finite difference method (FDM) is employed to simulate the dispersion of the detonation products into the surrounding air where the particles degenerate to marker points which track the moving interface between detonation products and air. The conversion between MPM and FDM is implemented by the projection between the particles… More >

  • Open Access

    ARTICLE

    An Optimal Preconditioner with an Alternate Relaxation Parameter Used to Solve Ill-Posed Linear Problems

    Chein-Shan Liu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.3, pp. 241-269, 2013, DOI:10.32604/cmes.2013.092.241

    Abstract In order to solve an ill-posed linear problem, we propose an innovative Jacobian type iterative method by presetting a conditioner before the steepest descent direction. The preconditioner is derived from an invariant manifold approach, which includes two parameters α and γ to be determined. When the weighting parameter α is optimized by minimizing a properly defined objective function, the relaxation parameter γ can be derived to accelerate the convergence speed under a switching criterion. When the switch is turned-on, by using the derived value of γ it can pull back the iterative orbit to the fast manifold. It is the… More >

  • Open Access

    ARTICLE

    Fracture & Fatigue Analyses: SGBEM-FEM or XFEM? Part 2: 3D Solids

    Leiting Dong1,2, Satya N. Atluri1,3

    CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.5, pp. 379-413, 2013, DOI:10.3970/cmes.2013.090.379

    Abstract The SGBEM-FEM alternating method is compared with the recently popularized XFEM, for analyzing mixed-mode fracture and fatigue growth of 3D nonplanar cracks in complex solid and structural geometries. A large set of 3D examples with different degrees of complexity is analyzed by the SGBEM-FEM alternating method, and the numerical results are compared with those obtained by XFEM available in the open literature. It is clearly shown that: (a) SGBEM-FEM alternating method gives extremely high accuracy for the stress intensity factors; but the XFEM gives rather poor computational results, even for the most simple 3D cracks; (b) while SGBEM-FEM alternating method… More >

  • Open Access

    ARTICLE

    Fracture & Fatigue Analyses: SGBEM-FEM or XFEM? Part 1: 2D Structures

    Leiting Dong1,2, Satya N. Atluri1,3

    CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.2, pp. 91-146, 2013, DOI:10.3970/cmes.2013.090.091

    Abstract In this paper, and its companion Part 2 [Dong and Atluri (2013b)], the Symmetric Galerkin Boundary Element Method (SGBEM), and the SGBEM-FEM alternating/coupling methods, are compared with the recently popularized Extended Finite Element Method (XFEM), for analyzing fracture and fatigue crack propagation in complex structural geometries. The historical development, and the theoretical/algorithmic formulations, of each method are succinctly reviewed. The advantages and disadvantages of each method are critically discussed. A comprehensive evaluation of the performances of the SGBEM-based methods, and their comparison with XFEM, in modeling cracked solid structures undergoing fatigue crack-growth is carried out. A thorough examination of a… More >

  • Open Access

    ARTICLE

    State Estimation of Unequipped Vehicles Utilizing Microscopic Traffic Model and Principle of Particle Filter

    Yonghua Zhou1, Xun Yang1, Chao Mi1

    CMES-Computer Modeling in Engineering & Sciences, Vol.89, No.6, pp. 497-512, 2012, DOI:10.3970/cmes.2012.089.497

    Abstract The movements of vehicles equipped with various positioning systems such as global and wireless positioning ones have provided beneficial channels to acquire abundant traffic flow information for total road network. However, not all vehicles are mounted with positioning systems and not all equipped positioning facilities are always active. This paper will address how to estimate the number and the states of unequipped vehicles through a series of observations on equipped ones. The proposed estimation process initiates employing the non-analytical microscopic traffic model for particle filter to estimate the number, positions and speeds of unequipped vehicles between an equipped one and… More >

  • Open Access

    ARTICLE

    High-order Alternating Direction Implicit Method Based on Compact Integrated-RBF Approximations for Unsteady/Steady Convection-Diffusion Equations

    N. Thai-Quang1, N. Mai-Duy1, C.-D Tran1, T. Tran-Cong1

    CMES-Computer Modeling in Engineering & Sciences, Vol.89, No.3, pp. 189-220, 2012, DOI:10.3970/cmes.2012.089.189

    Abstract In this paper, the alternating direction implicit (ADI) method reported in [You(2006)] for the convection-diffusion equation is implemented in the context of compact integrated radial basis function (CIRBF) approximations. The CIRBF approximations are constructed over 3-point stencils, where extra information is incorporated via two forms: only nodal second-order derivative values (Scheme 1), and both nodal first- and second-order derivative values (Scheme 2). The resultant algebraic systems are sparse, especially for Scheme 2 (tridiagonal matrices). Several steady and non-steady problems are considered to verify the present schemes and to compare their accuracy with some other ADI schemes. Numerical results show that… More >

  • Open Access

    ARTICLE

    A Method for the Detection of the Distance & Orientation of the Relief Well to a Blowout Well in Offshore Drilling

    Cui Li1, Deli Gao1, Zhiyong Wu1, Binbin Diao1

    CMES-Computer Modeling in Engineering & Sciences, Vol.89, No.1, pp. 39-56, 2012, DOI:10.3970/cmes.2012.089.039

    Abstract At present, a relief well is the most reliable method to control serious blowout accidents, and it is necessary to detect very accurately the relative position of the relief well and the blowout well. The detection tool should be capable of detecting directly the relative distance and direction between the relief well and the blowout well. Its detection accuracy should also meet the engineering demand of drilling a relief well. Using the working principle of a proposed detection tool, this paper analyzes the spread and attenuation laws of the current injected by a single-electrode or three-electrode array in the relief… More >

  • Open Access

    ARTICLE

    Darcy-Stokes Equations with Finite Difference and Natural Boundary Element Coupling Method

    Peng Weihong1, Cao Guohua2, Dongzhengzhu1, Li Shuncai3

    CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.3&4, pp. 173-188, 2011, DOI:10.3970/cmes.2011.075.173

    Abstract Numerical method is applied to investigate the Darcy-Stokes equations, which is governing the steady incompressible Stokes flow past a circular cavity in a porous medium. The free fluid flow is modeled by the incompressible Stokes equations, and the flow in the porous medium is imposed by Darcy equations. Based on domain decomposition method with D-N alternating iteration algorithm, the coupling method of finite difference method and natural boundary element method is studied for the coupling Darcy-Stokes equations under a certain pressure difference. The numerical results indicate that the finite difference and natural boundary element coupling method is efficient and convenient… More >

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